Method and apparatus for fluting a web in the machine direction

ABSTRACT

A forming device for gathering the width of a traveling web is disclosed. The forming device includes opposing arrays of flute-forming bars that can be interlaced to define therebetween a longitudinal flute-forming labyrinth effective to reduce the width of a web traveling therethrough by a preselected take-up ratio. The flute-forming bars are curved beginning at an entry end of the forming device such that they converge in a lateral direction as they proceed in the machine direction. In this manner, individual elements of the web traveling between the respective arrays in the machine direction follow contour lines along the curved bars or between adjacent ones of the curved bars so that no such element crosses any flute-forming bar in the cross-machine direction as the web travels and is fluted. A corrugating die for introducing a near-net shape to the intermediate-fluted web is also disclosed, as are a corrugating line incorporating these operations and methods for its operation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.14/271,206 filed May 6, 2014, which is a continuation of U.S.application Ser. No. 14/067,783 filed Oct. 30, 2013, which claims thebenefit of U.S. Provisional Patent Application Ser. No. 61/721,079 filedNov. 1, 2012, all of which are incorporated herein by reference.

BACKGROUND

Corrugated webs possess increased strength and dimensional stabilitycompared to un-corrugated (i.e. flat) webs of the same material. Forexample, corrugated paperboard or cardboard is widely used in storageand shipping boxes and other packaging materials to impart strength. Atypical corrugated cardboard structure known as ‘double-wall’ includes acorrugated paperboard web sandwiched between opposing un-corrugatedpaperboard webs referred to as ‘liners.’ The opposing liners are adheredto opposite surfaces of the corrugated web to produce a compositecorrugated structure, typically by gluing each liner to the adjacentflute crests of the corrugated web. This structure is manufacturedinitially in planar composite boards, which can then be cut, folded,glued or otherwise formed into a desired configuration to produce a boxor other form for packaging.

Corrugated webs such as paperboard are formed in a corrugating machinestarting from flat webs. A conventional corrugating machine feeds theflat web through a nip between a pair of corrugating rollers rotating onaxes that are perpendicular to the direction of travel of the web whenviewed from above. Each of the corrugating rollers has a plurality oflongitudinally-extending ribs defining alternating peaks and valleysdistributed about the circumference and extending the length of theroller. The rollers are arranged so that their respective ribs interlockat the nip, with the ribs of one roller being received within thevalleys of the adjacent roller. The interlocking ribs define acorrugating labyrinth through which the web travels as it traverses thenip. As the web is drawn through the corrugating labyrinth it is forcedto conform to the configuration thereof, thus introducing into the webflutes or corrugations that approximate the dimensions of the pathwaythrough the corrugating labyrinth. Accordingly, it will be appreciatedthat in a conventional corrugating machine flutes are introduced intothe web along a direction that is transverse to the web-travel pathway;i.e. the flutes extend in a transverse (cross-machine) directionrelative to the direction of travel of the web (machine direction). Moresimply, conventionally the flutes extend along the width of the webbetween its lateral edges. An example of this conventional methodologyis shown in U.S. Pat. No. 8,057,621 (see FIGS. 7 and 7 a thereof), whichis incorporated herein by reference.

Corrugating a web in this manner can damage the paperboard or other webmaterial because it introduces a substantial amount of oscillatoryfrictional and tension forces to the web leading into and whiletraversing the corrugating nip. Briefly, as the web is drawn between thecorrugating rollers and forced to negotiate the corrugating labyrinth,the tension of the web, as well as compressive stresses normal to theplane of the entering web, oscillate in magnitude and direction assuccessive flutes are formed due to the reciprocating motion of thecorrugating ribs relative to the web, and due to roll and drawvariations in the web through the labyrinth as it is being corrugated.The oscillatory nature of the web tension through a corrugatinglabyrinth between corrugating rollers is well documented; see, e.g.,Clyde H. Sprague, Development of a Cold Corrugating Process FinalReport, The Institute of Paper Chemistry, Appleton, Wis., Section 2, p.45, 1985. The resulting substantial cyclic peaks in web tensiontypically produce some structural damage in the web as it is corrugated.

In addition to undesirable tension effects, corrugating the web in thecross-machine direction introduces flutes that extend transverse to thefibers of the paperboard, which typically run the length of the web inthe machine direction. Thus, flutes formed in a cross-machine directionmust re-orient and introduce undulations into the paper fibers, whichcan also lead to reduced strength.

One way to address the aforementioned problems would be to corrugate theweb in the machine direction so that the flutes extend along thedirection of the web-travel pathway; i.e. in the longitudinal directionof the web itself. This is commonly referred to as ‘longitudinalcorrugating’ or ‘linear corrugating.’ One issue with longitudinalcorrugating is that as the longitudinally-extending flutes are formed,they necessarily consume web width (i.e. the extent of the web in thelateral, cross-machine direction) in order to convert the initially flatweb into one having hills and valleys. In other words, to producelongitudinally-extending flutes the web must be gathered in thecross-machine direction such that its overall width after the flutes areformed is lower than the web width prior to forming the flutes. Theratio of the flat web's original, pre-corrugated width to itspost-corrugated width is referred to as the ‘take-up ratio.’ Take-upratios are well known for standard flute sizes in conventionaltransverse corrugating methods. For example, a conventionaltransversely-corrugated, A-fluted web exhibits a typical take-up ratioof 1.56 because the amplitude and pitch of A-flutes are such thatintroducing them into the web reduces the web length (i.e. its lineardimension in a direction transverse to the flutes) by 64%; i.e. makingthe ratio of starting length to ending length equal to 1.56. Statedanother way, in conventional corrugating if one wants to end up with 100yards of transversely-corrugated web, one has to feed 156 yards of flatweb to the corrugating machine to account for the web length consumed byintroducing the A-flutes.

A similar take-up ratio will be present in linear corrugating exceptthat now that ratio will apply to the web's width in the cross-machinedirection instead of to its length. This introduces a special problembecause typical linear-corrugating devices such as linear-corrugatingrollers cannot simultaneously gather web width and introducecorrugations without damaging and tearing the web. For example, linearcorrugating rollers have circumferentially-extending ribs and valleysdistributed longitudinally along the length of the rollers, wherein thecircumferential ribs of one roller are received within thecircumferential valleys of the opposing roller, and vice versa. Unlessthe web width is condensed sufficiently to account for the take-up ratioof the finished product prior to entering the nip between these rollers,it will be substantially wider than the intended product on entering thenip and would need to be instantaneously and simultaneously gathered andcorrugated to produce the desired product. This cannot be achievedwithout damaging and tearing the web. To solve this problem, thetraveling web should be gathered from its initial width to itsapproximate final width, based on the anticipated take-up ratio, priorto being introduced into the linear-corrugating rollers or othercorrugating device.

For this reason, to date carrying out linear corrugating is impracticalfor commercial applications that require conventional flute sizes (e.g.A- through E-flutes) for useful web widths (e.g. final width of 50inches). U.S. Pat. No. 7,691,045 (incorporated herein by reference)discloses a machine for gathering a traveling web laterally in thecross-machine direction prior to introducing that web to a set ofrollers to introduce a three-dimensional pattern into the web. Thatmachine utilizes a series of opposed rollers disposed along the machinedirection for introducing longitudinal folds into the web beginning atthe web's center. Each successive set of rollers thereafter introducestwo additional folds at either side of the previously-made fold(s) untilthe entire web consists of a series of longitudinal folds or flutes sothat the web's entire width has been gathered to a desired degree. Thismachine can be effective to gather the width of a paper or other webprior to downstream operations (such as corrugating or otherthree-dimensional forming) for relatively narrow widths that are notparticularly useful on a commercial scale. Unfortunately, however, forcommercial widths of, e.g. 50 inches or greater, the number ofsuccessive sets of opposed rollers that would be needed to successivelyform the longitudinal flutes is such that the machine would beimpractically long, producing a very large footprint. Accordingly, sucha machine is not capable of being retrofitted into existing corrugatinglines where space is tight, and for new installations it would take uptoo much space to be practical.

U.S. Pat. Appl'n Pub. No. 2010/0331160 (incorporated herein byreference), which is commonly assigned with the present application,discloses another machine for gathering the width of a traveling web.That machine utilizes opposing sets of linear flute-forming bars thatgenerally extend in the machine direction, wherein the spacing betweenadjacent ones of the bars generally decreases along the machinedirection. The opposing sets of bars are interlaced such that thetraveling web is caused to gradually conform to an intermediatelongitudinally-fluted geometry as it passes between the opposing sets ofbars by virtue of the decreasing lateral spacing between the bars. Thismachine has the advantage that it is capable of gathering the width of atraveling web in a relatively short distance of web travel, and istherefore of a practical size and footprint to be retrofitted intoexisting installations. However, as the paperboard web traverses thelabyrinth between the opposing sets of flute-forming bars and isgathered laterally inward, individual paper elements in the web aredragged laterally across the bars thereby introducing position- andtime-dependent lateral tension variations and oscillations throughoutthe web, which are undesirable and may contribute to damage.

It would be desirable to gather the width of a traveling web of materialin the cross-machine direction according to a predetermined take-upratio desirable for downstream processing, while minimizing oreliminating introduction of lateral tension or frictional forces in theweb as a result of the gathering operation. The gathered web could thenbe introduced into downstream processing operations, such aslongitudinal corrugating or other operations for introducingthree-dimensional structure to the web, which downstream operation(s)will benefit from the lateral take-up ratio introduced in the earliergathering operation.

SUMMARY OF THE INVENTION

A forming device is disclosed, which has an entry end and an exit endspaced apart along a machine direction. The forming device includes aplurality of flute-forming bars extending from adjacent the entry towardthe exit end. At least a subset of the plurality of flute-forming barsare curved such that they converge in a cross-machine direction as theyproceed toward the exit end.

A corrugating die is also disclosed, which has an entry end and an exitend spaced apart along a machine direction. The corrugating die has acontinuous smooth first forming surface having a first sinus contourviewed in lateral cross-section adjacent the entry end. The firstforming surface gradually evolves in the machine direction to a secondsinus contour viewed in lateral cross-section adjacent the exit end. Thefirst sinus contour has a larger amplitude and lower frequency than saidsecond sinus contour.

A corrugating line is also disclosed, which includes the aforementionedforming device located upstream along the machine direction of theaforementioned corrugating die. The forming device is configured todeliver from its exit end a formed web of medium material that has beenfluted to an intermediate longitudinally-fluted geometry. Thecorrugating die is configured to receive the formed web and to convertit from the intermediate longitudinally-fluted geometry to a near netshape having a lower-amplitude, higher-frequency fluted geometry thatapproximates a final desired corrugated geometry.

A method of forming a longitudinally-corrugated web is also disclosed.The method includes the following steps: uniformly introducing into aweb of medium material a full-width array of longitudinal flutes ofintermediate geometry as the web travels along a web-travel pathway in amachine direction, thereby reducing the width of the web tosubstantially a final width that corresponds to a take-up ratio forpreselected longitudinal corrugations or other three-dimensionalstructure to be formed in the web at the aforementioned final width,wherein substantially no portion of the web traverses a flute-formingelement in a cross-machine direction while introducing theintermediate-geometry flutes therein.

A further method of forming a longitudinally-corrugated web is alsodisclosed, which includes the following steps: feeding a web of mediummaterial having an initial width in a machine direction through alongitudinal fluting labyrinth defined between opposing sets of at leastpartially interlaced flute-forming bars, wherein pluralities of theflute-forming bars in each set are curved such that the bars in saidrespective pluralities converge in a cross-machine direction as theyproceed toward an exit end; and reducing the width of the web to asubstantially final width by forming longitudinal flutes of intermediategeometry in the web as it passes through the labyrinth, whereinindividual elements of the web passing through the labyrinth followcurved contour lines along respective individual ones of the pluralitiesof flute forming bars from a point where the respective element firstcontacts the respective bar all the way until the web exits thelabyrinth.

A further forming device is disclosed, which has an entry end and anexit end spaced apart along a machine direction, and a plurality offlute-forming bars extending from adjacent the entry end toward the exitend. At least a subset of the plurality of flute-forming bars each has avariable-tangent configuration such that imaginary tangents to each ofthe subset of bars, at spaced locations along a length thereof, becomesuccessively nearer to parallel with the machine direction. In thismanner the subset of flute-forming bars converge in a cross-machinedirection as they proceed toward the exit end.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic illustration of a longitudinal corrugating lineincorporating a forming device and a longitudinal corrugating die asdisclosed herein.

FIG. 2 is a perspective view of a forming device for use in alongitudinal corrugating line, wherein respective first (upper) andsecond (lower) arrays of flute-form ing bars are spaced apart from oneanother.

FIG. 2a is a close-up view showing details of flute-forming bars at theexit end of the forming device of FIG. 2.

FIG. 3 is a perspective view of the forming device of FIG. 2, whereinthe first and second arrays of flute-forming bars have been partiallyengaged to interlace the opposing flute-forming bars beginning at alocation intermediate the entry and exit ends of the forming device,with the degree of interlacement increasing in the machine directiontoward the exit end.

FIG. 3a is a close-up view showing details of interlaced flute-formingbars at the exit end of the forming device of FIG. 3.

FIGS. 4a and 4b are views of the respective first and second sets offlute-forming bars secured to respective first and second frames, eachviewed along a line that is perpendicular to the respective frame andfacing the associated set of bars.

FIG. 4c is a schematic view of an array of flute-forming bars asdescribed herein, e.g. of one of the arrays illustrated in FIGS. 4a and4b , illustrating the constant lateral spacing between laterallyadjacent flute-forming bars in each array.

FIG. 5 is a schematic plan view of both the first and second sets offlute-forming bars as disclosed herein at least partially interlacedwith one another. The figure also schematically illustrates gatheringweb width using the disclosed forming device to accommodate take-upratios associated with conventional “A” and “C” flutes for longitudinalcorrugating.

FIG. 6 is a lateral cross-section of a flute-forming bar used in aflute-forming device as disclosed herein, taken along line 6-6 in FIG.2.

FIG. 7 is a side view of a forming device as disclosed herein, shownduring a state of operation, e.g. with the arrays of flute-forming barsengaged as in FIG. 3.

FIG. 7a is a perspective view of the forming device in FIG. 7 shownduring the same state of operation.

FIG. 8 illustrates an alternative embodiment of a forming device asherein disclosed, where the forming device defines an intermediatelongitudinal corrugating labyrinth that follows a curved path in ordereffect web-course adjustment at the same while introducing intermediatecorrugations to gather web width prior to downstream operations.

FIG. 8a is a side view of the forming device of FIG. 8, shown along line8 a-8 a in FIG. 8.

FIG. 9a is a perspective sectional view of a corrugating die asdisclosed herein for converting a formed web exiting the disclosedforming device to near net shape compared to a final desired corrugatedgeometry.

FIG. 9b is a perspective view of the corrugating die in FIG. 9a whereinthe respective die halves 310 and 320 have been engaged.

FIG. 9c is an end view of the corrugating die as shown in FIG. 9c ,showing the tapered configuration of the ribs defining the initial sinusgeometry of the web pathway through the corrugating die.

FIG. 10 is a perspective view, in section, of a portion of a travelingweb as it is formed into near net shape in the corrugating die describedherein, from the intermediate-corrugated web produced in the formingdevice.

FIG. 11 is a perspective view showing longitudinal corrugating rollersengaged to define a corrugating nip therebetween for impartinglongitudinal corrugations to a passing web.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

FIG. 1 schematically illustrates a longitudinal corrugating line 1000.In the illustrated embodiment the corrugating line 1000 includes, in themachine direction along the web-travel pathway of a web 10 ofcorrugating medium, a preconditioning apparatus 100, a forming device200, a corrugating die 300 and a final corrugating apparatus 400. InFIG. 1, a single web 10 of corrugating medium is traveling along theweb-travel pathway through the corrugating line 1000 in the machinedirection. The web is denoted by reference numerals 10, 10 a, 10 b, 10 cand 10 d in FIG. 1, corresponding to different stages in the line 1000wherein the web has been conditioned or treated or manipulated indifferent operations as more fully described below.

Briefly, in FIG. 1 the web 10 is initially fed from a source ofcorrugating medium (e.g. from rolls as is conventional in the art, notshown) to the preconditioning apparatus 100. In the preconditioningapparatus 100, the moisture and/or temperature of the web 10 can beadjusted to be within an optimum range if desired. Thereafter, theconditioned web 10 a is fed to a forming device 200. In the formingdevice 200, the overall width of the traveling web is reduced bygathering the web laterally (in the cross-machine direction) viaintroduction of longitudinally-extending flutes to produce a formed web10 b of intermediate geometry. The longitudinally-extending flutes inthe formed web 10 b are of larger amplitude and lower frequency thanthose of the final corrugated web 10 d to be made downstream. Byintroduction of the intermediate-geometry flutes, the forming device 200reduces the width in the formed web 10 b (in the cross-machinedirection) compared to the original web 10 (or conditioned web 10 a) bythe take-up ratio (or by approximately that ratio) corresponding to thefinal longitudinal flutes that are to be introduced downstream.Importantly, the overall width of the formed web 10 b emerging from theforming device 200 will approximate or be substantially the same as thewidth of a final corrugated web 10 d.

Each of the aforementioned operations will now be described.

Preconditioning Apparatus

Beginning first with the preconditioning apparatus 100, preconditioningis optional and may not be necessary or desirable in every longitudinalcorrugating line 1000. Accordingly, the preconditioning apparatus may beomitted. When included, the preconditioning apparatus 100 can be used tointroduce or adjust a moisture content in the web 10 prior to itsentering the forming device 200. Any conventional or suitable device forproviding or adjusting the moisture in the web can be utilized in or asthe preconditioning apparatus 100, such as spray nozzles,moisture-application rollers, etc. These will not be described furtherhere, but exemplary moisture-conditioning devices suitable in thepreconditioning apparatus are known, for example, from U.S. Pat. No.8,057,621, incorporated above.

The preconditioning apparatus 100 may also include one or more devicesto adjust the temperature of the traveling web 10 into an optimum rangefor downstream processing. For example, heated rollers and hot platesare conventional in the art and might be used. In some embodiments bothmoisture and temperature can be adjusted contemporaneously orsuccessively via the preconditioning apparatus 100 in order toprecondition the web for downstream operations. For example, it isgenerally desirable for the traveling web to possess between 6 and 9weight percent moisture to protect the paper fibers. Heating the web toan elevated temperature (particularly in cold climates) but notsufficiently high to burn or otherwise damage the paper can also helprelax paper fibers making them less susceptible to breakage or damagefrom folding and tension effects introduced in downstream corrugatingoperations. Both moisture- and temperature-preconditioning operationsare described in the aforementioned '621 patent and elsewhere in theliterature, and they will not be described further here.

Forming Device

Once the web 10 has been treated to produce the preconditioned web 10 a,that web (or in the absence of preconditioning apparatus 100, theunconditioned web 10) is fed along the web-travel pathway into theforming device 200. An example embodiment of the forming device 200 isillustrated in FIG. 2. In that embodiment the forming device has a firstor upper set of flute-forming bars 210 and a second or lower set offlute-forming bars 220. The sets of flute-forming bars 210 and 220 aredisposed opposite and facing one another on either side of theweb-travel pathway through the forming device 200. In FIG. 2, each ofthe opposed sets of flute-forming bars 210 and 220 is provided as asubstantially planar array of respective first or second flute-formingbars 212 or 222 supported on a respective first (or upper) or second (orlower) frame 215 or 225. The frames 215 and 225 are secured to forwardand rear support posts 230 and 235 to fix the relative positions andorientations of the frames 215 and 225 (and correspondingly of the firstand second sets/arrays of flute-forming bars 210 and 220) relative toone another. In the illustrated embodiment, the lower frame 225 issecured to the support posts 230,235 in a fixed position such that it issubstantially parallel to the web-travel pathway through the formingdevice 200 and so that its height or position is fixed. The upper frameis secured at its exit end 202 to the forward support posts 230 viaposition-adjustment actuators 240 capable of adjusting the position orspacing of the upper frame 215 relative to that of the lower frame 225at the exit end 202 of the forming device 200. The actuators 240 can be,for example, hydraulic or pneumatic pistons, stepper motors, servos,solenoids, or any other suitable or conventional device capable toadjust the position of the upper frame 215 relative to the lower frame225 at the exit end 202.

In a preferred embodiment, the upper frame 215 is similarly secured tothe rear support posts 235 via adjustment actuators 240 as describedabove, so that the position or spacing of the upper frame 215 issimilarly adjustable relative to the lower frame 225 at the entry end201. Indeed, in preferred embodiments both the entry and exit ends ofthe upper/first frame 215, and therefore of the upper/first set offlute-forming bars 210, are independently adjustable toward and awayfrom (e.g. height adjustable relative to) the lower/second frame 225,and therefore lower/second set of flute-forming bars 220. In analternative embodiment, both the first and second frames 215 and 225 canbe independently position-adjustable using similar actuators asdescribed above, or adjustable relative to the opposed frame, at one orboth of the entry and exit ends 201 and 202 of the forming device.

FIGS. 4a and 4b illustrate the respective upper and lower frames 215 and225 and the associated arrays of flute-forming bars 210 and 220 along aline normal to the respective frame and viewed from a position betweenthe respective arrays 210 and 220. As best seen in these figures, eachplanar array (set) of flute-forming bars 210 and 220 is arranged suchthat the associated bars 212 and 222 all generally extend along themachine direction from the entry end 201 toward the exit end 202 of theforming device 220. Individual ones of the flute-forming bars 212 and222 in each array are curved along at least rear portions or segmentsthereof such that they converge laterally (in the cross-machinedirection) as the bars 212 and 222 proceed in the machine direction fromthe entry end 201 toward the exit end 202. As used herein, the term‘converge’ means to approach or to become closer together, withoutrequiring that the converging elements actually meet. As will becomeevident below, it is in fact preferred that convergent flute-formingbars as described herein do not actually meet, but instead tend towardand ultimately reach parallel paths. In an embodiment, ones of the bars212 and 222 cease to curve at a location approaching the exit end 202 ofthe forming device such that all of the bars 212 and 222 in that deviceare substantially parallel along the machine direction from thatlocation forward, until the exit end 202. Alternatively, the curved barsmay be technically curved all the way up to the exit end 202, althoughtangents to all of the bars 212 and 222 preferably are substantiallyparallel to one another along the machine direction at that end 202.More broadly, the convergent flute-forming bars 212 and 222 arecharacterized by a variable-tangent configuration, wherein imaginarylines drawn tangent to each of the bars at spaced locations along thebar's length become successively nearer to parallel with the machinedirection along which a web will travel between the entry end and theexit end 202. A continuously-curved flute-forming bar 212,222, or acontinuously-curved rear region (adjacent the entry end 201) thereof, asdescribed in detail herein is preferred for the variable-tangentconfiguration. But other variable-tangent shapes may be possible. Theabove features are all more fully described below.

Returning to the preferred embodiment illustrated in FIGS. 4a and 4b ,individual bars 212 and 222 in the respective arrays are curved suchthat they converge toward an imaginary line 209 or 229 in the plane ofthe associated array that runs along the web-travel pathway parallel tothe machine direction in the forming device. Most preferably, thatimaginary line 209 or 229 represents a centerline of the respectivearray as illustrated in the figures, such that at least portions of theindividual flute-forming bars 212,222 on either side of the centerlinein the respective array 215,225 are curved such that they approach thatcenterline as they extend in the machine direction. In an exemplaryembodiment, one or more of the forming bars 212,222 can exhibit aparabolic curvature, or all of the curved bars 212,222 can exhibitparabolic curvature, between the entry and exit ends 201 and 202.

In the illustrated embodiment the upper array 210 has an odd number offlute-form ing bars 212 (15 are illustrated) and the lower array 220 hasan even number of flute-forming bars 222 (16 are illustrated). Thisarrangement permits the respective arrays to be interlaced with oneanother to define an intermediate longitudinal fluting labyrinth 250(seen in FIG. 7) for a web 10 of material traveling through the formingdevice 200 (described below), while also permitting both arrays to becentered along a common centerline (viewed from above), e.g. along acenterline of the web-travel pathway, while interlaced. However, it willbe appreciated that both the upper and lower arrays 210 and 220 cancomprise odd or even numbers of flute-forming bars (for example, botharrays can include the same number of flute-forming bars), with thecaveat that they could not then both be aligned along a commoncenterline (viewed from above) while interlaced.

Returning to the figures, when an array of flute-forming bars has an oddnumber of such bars, e.g. bars 212 in the upper array 210 illustrated inFIG. 4a , the centermost flute-forming bar 212 a preferably is linearand aligned collinearly with the centerline 209 of the array 210. Thiscenterline also preferably coincides with a centerline of the lowerframe 225 and therefore of the forming device 200. More broadly, in anarray of forming bars as disclosed herein, it is preferred that the onlytime one of the forming bars is linear and not curved along at least asegment thereof from the entry end 201 toward the exit end 202 is whenthat forming bar is aligned and co-linear with the imaginary line towardwhich the other forming bars in the same array will converge as theyextend toward the exit end 202. All other forming bars in the same arraywill be curved at least in rear portions or segments thereof so as tolaterally converge on that imaginary line, and in this case also on thelinear forming bar co-linear with said imaginary line.

This can be seen in the upper array 210 illustrated in FIG. 4a , whereinthe centermost forming bar 212 a is linear, and moreover is co-linearwith the imaginary centerline 209 of the array 210. A first pair offorming bars 212 b are disposed on either side of and spaced laterallyfrom the centermost bar 212 a, each extending from the entry end 201toward the exit end 202 of the forming device 200, and each being curvedsuch that it converges on the centerline 209 (and on the centermostforming bar 212 a) as it proceeds toward the exit end 202. A second pairof forming bars 212 c are disposed on either side of and spacedlaterally from the first pair of forming bars 212 b, again eachextending from the entry end 201 toward the exit end 202 of the formingdevice, and each being curved such that it converges on the centerline209 (and on the centermost forming bar 212 a) as it proceeds toward theexit end 202. A third pair of forming bars 212 d are disposed on eitherside of and spaced laterally from the second pair of forming bars 212 c,again each extending from the entry end 201 toward the exit end 202 ofthe forming device, and again each being curved such that it convergeson the centerline 209 (and on the centermost forming bar 212 a) as itproceeds toward the exit end 202. Additional pairs of forming bars 212d-h spaced at successively greater intervals from the centerline can beprovided in the array 210.

Turning now to the lower array of flute-forming bars 220 illustrated inFIG. 4b , there is no centermost flute-forming bar 222. This is becausethere are an even number of flute-forming bars 222. Instead thecentermost pair of flute-forming bars 222 a are each spaced on eitherside of the centerline 229, with successively more laterally-distantpairs of the flute-forming bars 222 b-h being likewise spaced on eitherside of the centerline 229. Similarly as for the upper array 210, herethe second pair of forming bars 222 b are disposed on either side of andspaced laterally from the first pair of forming bars 222 a, eachextending from the entry end 201 toward the exit end 202 of the formingdevice, and each being curved such that it converges on the centerline229 of the lower array 220 as it proceeds toward the exit end 202. Thesuccessive third through eighth illustrated pairs of lower flute-formingbars 222 c-h are likewise successively laterally spaced from thenext-centermost pair, and are likewise curved such that each convergeson the centerline 229 of the lower array 220 toward the exit end 202 ofthe forming device 200.

Still referring to FIGS. 4a and 4b , for each of the arrays 210 and 220the degree of curvature of the associated flute-forming bars 212 and 222is the greatest at the entry end 201 of the forming device 200, where aweb of medium material would first enter that device 200. The degree ofcurvature of the flute-forming bars gradually decreases as the barsproceed toward the exit end 202, from which a formed web 10 b (see FIG.7a ) would emerge during a longitudinal corrugating process. The resultis that individual flute-forming bars 212 and 222 converge rapidlytoward the imaginary centerline (or other longitudinal line) in therespective array 210 or 220 adjacent the entry end 201 of the formingdevice. However, as the degrees of curvature of the bars decrease in themachine direction, so does the rate of convergence of the flute-formingbars gradually decrease, preferably until all the bars 212 or 222 in therespective array 210 or 220 become generally linear and parallel to oneanother in the machine direction at the exit end 202 of the formingdevice 200. That is, the bars 212 and 222 can cease to be curved at alocation approaching the exit end 202, beyond which they are allgenerally linear and parallel as described above. Alternatively, thebars 212 and 222 may continue to be curved up to the exit end 202 of theforming device 200, wherein the degree of curvature will preferably besubstantially reduced at the exit end 202 compared to the entry end 201so that at the exit end 202 they are all approximately linear andparallel. In any event tangents of all the flute-forming bars 212 and222 at the exit end 202 are all substantially parallel along the machinedirection.

As illustrated schematically in FIG. 4c , for a given array 210 or 220it is preferred that the flute-forming bars 212 or 222 in that array aresubstantially equidistant at any given location along the machinedirection in the forming device 200. For example, FIG. 4c schematicallyillustrates three longitudinal locations along the machine direction, A,B and C, such that the lateral distances between adjacent ones of theflute-forming bars are all equal at the respective locations. That is,the lateral distances a₁, a₂ and a₃ between adjacent flute-forming barsat machine-direction location A are all equal, and likewise formachine-direction locations B (distances b₁, b₂ and b₃) and C (distancesc₂ and c₃). In preferred embodiments, the above holds true for both ofthe first and second (upper and lower) arrays of flute-forming bars 210and 220 in the forming device 200.

It will be appreciated, again with reference to FIG. 4c (and also FIGS.4a and 4b ), that while the flute-forming bars in a given array arepreferably all equidistant any given location along the machinedirection, the lateral distance between adjacent bars decreases as thebars proceed in the machine direction toward the exit end 202 of theforming device, at least along rear segments or portions of the bars.That is, referring to FIG. 4c , a₁>b₁>c₁ at least in rear convergentsegments or portions of the flute-forming bars 212,222, consistent withthe fact that those bars preferably laterally converge as they proceedin the machine direction toward the exit end 202. In preferredembodiments, that convergence is the result the lateral curvature of atleast a subset (e.g. all but the center-most) of the flute-forming bars212,222 in each array 210 or 220 as discussed above. More broadly,however, it will be understood that the noted subset of flute-formingbars 212,222 have a variable tangent configuration, such that imaginarytangents to each of those flute-forming bars, drawn at spaced locationsalong the length of each such bar, become successively nearer toparallel with the machine direction as that bar proceeds toward the exitend 202 of the forming device. This is illustrated schematically in FIG.4c , wherein for a given flute-forming bar 212, 222 a tangent line T_(a)drawn at machine-direction location “A” remote from the exit end is notparallel with the machine direction; i.e. with the centerline in thatfigure. Whereas, a tangent line T_(b) drawn at location “B” nearer tothe exit end is closer to parallel with the machine direction, and atangent line T_(c) drawn at location C essentially at the exit end isparallel or approximately parallel to the machine direction. In thepreferred embodiments described here and illustrated in the figures,each of the flute-forming bars 212,222 having the aforementionedvariable tangent configuration is continuously and smoothly curved inits variable-tangent region, which may be a rear portion of the bar orit may be the full length of the bar. Alternatively and less preferably,the variable-tangent region may be formed as a series of linear orstepped forming-bar segments that together integrate to or approximate acurve (not shown) beginning adjacent the entry end and extending towardthe exit end 202.

Returning to FIG. 2 and referring now to FIG. 3, the respective andopposed first and second arrays 210 and 220 of flute-forming bars areconfigured so that on approaching one another they become interlaced inorder to define an intermediate longitudinal fluting labyrinth 250therebetween. In FIG. 3, the position of the upper frame 215 has beenadjusted toward the lower frame 225 at the exit end 202 to interlace theforward portions of the opposing flute-forming bars 212 and 222 at theexit end 202 and in the exit region of the forming device 200. In thesame figure, the upper frame 215 has also been adjusted toward the lowerframe 225 at the entry end 201, although to a lesser degree than at theexit end 202, in order to adjust the location of the choke point 290(FIG. 7) at which the opposing flute-forming bars 212 and 222 just beginto interlace as described more fully below. In a preferred embodiment,the curvatures of the respective flute-forming bars 212 and 222 in theopposing arrays 210 and 220 are such that the interlaced flute-formingbars 212,222 are equidistant or substantially equidistant from oneanother at any given longitudinal location along the machine directionin the forming device 200, and such that curved ones thereof allsimilarly converge laterally toward a common imaginary line (preferablya centerline) parallel to the machine direction in the forming device.

FIG. 5 is a schematic plan view illustrating the interlaced upper andlower sets 210 and 220 of flute-forming bars 212 and 222, wherein upperbars 212 are represented by solid contour lines and lower bars 222 arerepresented by partially broken contour lines. It will be appreciatedthat the contour lines representative of alternating upper and lowerflute-forming bars 212 and 222 are similar to the contour linesillustrated in FIG. 4c for only one array of those bars. Indeed, theinterlaced array in FIG. 5 exhibits similar features. Namely, thedegrees of curvature (and therefore the rate of convergence) of curvedinterlaced flute-forming bars 212,222 in FIG. 5 decrease as the barsproceed in the machine direction toward the exit end 202, at least inrear portions of the bars. The lateral spacing between adjacent ones ofthe interlaced bars 212,222 is also preferably constant (i.e. all theinterlaced bars are preferably substantially equidistant) at any givenlongitudinal location along the machine direction, with said spacingbecoming gradually smaller as one proceeds in that direction.Preferably, the flute-forming bars 212,222 in the interlaced array inFIG. 5 (and also seen in perspective view in FIG. 3) also are allgenerally linear and parallel to one another in the machine direction inan exit region of the forming device; i.e. adjacent the right-hand sideof each of FIGS. 3 and 5.

Turning to FIG. 6, an exemplary flute-forming bar 212/222 is shown inlateral section. In the illustrated embodiment, the forming bar 212/222includes a base portion 260 and a web-engagement portion 262. Ininterlaced portions of the opposing sets of flute-forming bars 210 and220 in operation, the respective engagement portions 262 of one set ofbars are received in the lateral spaces defined between adjacentengagement portions 262 of the flute-forming bars in the opposing set.This can be seen most clearly in FIG. 3a . The flute-forming bars212/222 can be secured directly to the associated frame 215,225.Alternatively, and particularly when a high degree of interlacement or(i.e. the degree to which the engagement portions 262 of the first setof bars 210 penetrates beyond an imaginary plane tangent to theoutermost surfaces of the engagement portions 262 of the second set 210,and vice versa) may be desired, the flute-forming bars 212,222 can beformed or secured to spacers 270 to increase the distance between theweb-engagement portion and the associated frame 215,225. Theflute-forming bars 212,222 can be secured to the spacers 270 in anyconventional or suitable manner, e.g. via welding, brazing, adhesives ormechanical fasteners using appropriate gaskets to ensure a fluid-tightseal. Alternatively the flute-forming bars 212,222 can be formedintegrally with the associated spacers 270, effectively resulting in arelatively tall flute-forming bar 212,222.

In operation web-engagement portion 262 of the flute-forming bar 212,222engages a traveling web 10 in the forming device to thereby formintermediate longitudinal flutes therein to produce the formed web 10 b(see FIG. 7a ). Accordingly, the engagement portion 262 preferably has agenerally rounded (e.g. cylindrical) surface for contact with the web10. The engagement portion 262 surface can include an anti-frictionsurface feature to thereby reduce the frictional forces on the web 10 asit passes between the interlaced first and second sets of flute-formingbars 210 and 220 to introduce the intermediate fluted geometry thereto(i.e. as the web 10 b is formed) in the forming device 200. In oneexample, the flute-forming bars 212,222 or portions thereof can bezero-contact bars operable to support the web 10 of medium material at avariable height thereabove on a cushion of air or other fluid that isemitted through fluid ports 205 provided in the engagement portions 262.Preferably the ports 205 are distributed over the engagement portions262 of the forming bars 212,222 substantially along their entirelengths, or at least along the portions thereof that will engage atraveling web 10 during use.

When the flute-forming bars 212,222 are operated as zero-contact bars,preferably the engagement portion 262 of each zero-contact bar has afluid passageway 204 therein in fluid communication with the fluid ports205 for conducting the desired fluid (such as air) to those ports 205.The fluid exits those ports 205 to thereby provide a cushion of thefluid between the engagement portion 262 surface and the web 10 in orderto support the traveling web 10 above the engagement portion 262 andthereby reduce or minimize friction as the web passes over the bars212,222. Preferably, the fluid cushion permits frictionless support ofthe web as it travels through the intermediate fluting labyrinth 250between the opposed forming bars 212,222.

Returning to FIG. 6, the fluid passageway 204 preferably is in fluidcommunication with a spacer passage 203 at the interior of the spacer270 on which it is secured, e.g. via a passage 202 in the base 260 ofthe forming bar 212,222. In this embodiment, the flute-forming bars212,222 can be extruded or gun drilled to provide the fluid passageway204 and passage 202. When formed together with the spacer 270, theentire assembly can be prepared as a single extrusion so that the spacerpassage 203, passage 202 and fluid passageway 204 cooperate to form adistribution manifold for the associated forming bar 212,222 to deliverfluid through the holes 205 therein.

As seen in FIGS. 2 and 6, at least one supply manifold 280 for thecushioning fluid can be provided on the surface of the upper frame 215opposite the surface where the flute-forming bars 212 are mounted. Thesupply manifold(s) 280 can be in the form of a U-shaped channel havingclosed ends, with the open face of the channel facing and being sealedto the surface of the frame 215 in order to define a supply passage 282for fluid as seen in FIG. 6. The supply passage 282 communicates withthe aforementioned spacer passage 203 (or directly with the passage 202when no spacer 270 is used) for each flute-forming bar 212 via a supplyopening 283 drilled or otherwise formed in the frame 215. As will beappreciated, the frame 215 can have a plurality of supply openings 283communicating with the supply passages 282 of each supply manifold 280,corresponding to and laterally aligned with the number and locations offlute-forming bars 212 at the opposite surface of the frame 215. Themanifold 280 can be secured to the frame 215 surface via conventional orsuitable means, for example via welding or brazing to provide acontinuous airtight seal, or using other mechanical fasteners with asuitable gasket to likewise ensure a tight seal. The fluid can besupplied to the manifold 280 via a conventional fitting 285 (seen inFIG. 2). As also seen in FIG. 2, a plurality of supply manifolds 280 canbe distributed along the machine direction. These plurality of manifolds280 can be connected to a common fluid source to supply the same fluid(including flow rate and pressure) at all three locations, or they canbe connected to different fluid sources, or each can be independentlyregulated, to deliver different fluids or different flow rates andpressures at different machine-direction locations as more fullydescribed below.

Although the foregoing description of the supply manifold(s) 280 wasgiven and illustrated with respect to the first frame 215 to which aremounted the first set of flute-form ing bars 210, the identicalarrangement can be incorporated for the second frame 225 in order tosupply a cushioning fluid to the flute-forming bars 222 in the secondset of said bars 220.

In one embodiment, all of the flute-forming bars 212,222 in both theupper and the lower arrays 210 and 220 can be supplied from a commonfluid source and regulated from a common single metering or throttlingvalve located upstream of both the respective supply manifolds 280 (e.g.one manifold 280 for each set of forming bars 210 and 220). In thisembodiment, a single supply manifold 280 can be used for each of theupper and lower arrays 210 and 220 (i.e. affixed to each of therespective upper and lower frames 215 and 225). Alternatively,respective pluralities of manifolds 280 can be positioned and used inconnection with each set 210 and 220 of flute-forming bars, allconnected in parallel to a commonly-regulated fluid source. In boththese embodiments the pressures and flow rates of the supportive fluiddelivered to all the bars 212,222 would be commonly controlled,resulting in substantially uniform pressures and flow rates of thatfluid through the holes 205 in all the flute-forming bars 212,222.

Alternatively, the respective manifold(s) 280 associated with each set210 or 220 of flute-forming bars 212 or 222 could be fitted withits/their own dedicated device for regulating pressure and flow rate ofthe fluid. Suitable regulation devices include, for example, metering orthrottling valves, pressure controllers, mass-flow controllers or somecombination of these. For example, a pressure regulator or mass-flowcontroller could be mounted in-line with the fitting(s) 285 of therespective manifold(s) 280 associated with only one set of flute-formingbars 212 or 222, between the fitting(s) and the fluid source. Thisembodiment would provide common control and substantially uniformpressures and flow rates for web-supporting fluid through all of theflute-forming bars 212 in the first set 210 thereof secured to the firstframe 215, and separately for all the flute-forming bars 222 in thesecond set 220 thereof secured to the second frame 225. In other words,the flow rates and fluid pressures would be substantially uniform ineach array of flute forming bars 210 and 220, but the flow rates andpressures in the first array 210 could be regulated independently of theflow rates and pressures in second array 220 and vice versa. This may bedesirable, for example, for dense, heavy webs traveling in a horizontalmachine direction, where additional pressure from the bottom might beuseful to support the traveling web 10 centrally and against the actionof gravity within the longitudinal fluting labyrinth 250. Alternatively,when the forming device 200 has a fluting labyrinth 250 that follows acurved pathway (described below) additional pressure may be desired fromthe side of the web 10 outside the direction the web must turn as itfollows the web-travel pathway through the curved labyrinth 250.

In a further alternative embodiment, successive supply manifolds 280distributed along the machine direction of the forming device 200 can beindependently connected in fluid communication with respective andisolated longitudinal zones or segments of the flute-forming bars 212 or222 secured to the associated frame 215 or 225. For example, one or aplurality of the flute-forming bars 212,222 can be provided in segmentsor having segmented distribution manifolds (e.g. segmented fluidpassageways 204 and cooperating spacer passageways 203 if present),wherein each segment of the bar 212,222 or its distribution manifoldcorrelates to a longitudinal zone of the forming device 200 extendingonly partway of the full longitudinal extent of that bar (including allof its segments) along the machine direction. In this embodiment,different pressures and flow rates of web-supporting fluid, or evendifferent fluids, can be distributed to the flute-forming bars 212,222to be emitted via fluid ports 205 at different longitudinal zones in theforming device 200. This may be desirable in order to successivelyincrease the amount of force normal to the planar extent of the webimparted thereto by supportive fluid emitted along the lengths of theflute-forming bars 212,222. For example, the pressure (normal to theplanar extent of the web) required to induce bending of that web arounda radius of curvature following one of the bars 212,222 can berepresented by the following relation:

$P = \frac{{Force}\mspace{14mu} {to}\mspace{14mu} {bend}\; \left( \frac{{lb}_{f}}{{inches}\mspace{14mu} {width}} \right)}{{Radius}\mspace{14mu} {of}\mspace{14mu} {curvature}\; ({inches})}$

As will be appreciated, the radii of curvature of the web at fixed weblocations gradually decrease as longitudinal flutes are formed while theweb travels in the machine direction through the labyrinth 250 betweenincreasingly interlaced forming bars 212,222. From the foregoingrelation and assuming a uniform web, as the radii of curvature decreasethe amount of pressure needed to sustain that curvature will increaseproportionately. Therefore, by increasing the fluid pressure emittedfrom fluid ports 205 at successive longitudinal zones in the machinedirection, one can conserve fluid and pumping power at upstreamlongitudinal locations where a relatively high degree of pressure is notrequired to sustain the web in spaced relation to the adjacentflute-forming bars 212,222. The degree of fluid pressure and its flowrate can thus be increased at successive longitudinal zones whereincreased pressure may be required to sustain the web in spaced relationto the bars 212,222 at greater degrees of fluting; i.e. lower radii ofcurvature in the formed/forming flutes. In this embodiment, therespective supply manifolds 280 connected in fluid communication to theopposing flute-forming bars 212 and 222 in the same longitudinal zonecan be supplied in parallel from the same fluid source and commonlyregulated. This will ensure common fluid pressures and flow rates fromboth the first and second sets 210 and 220 of flute-form ing bars in thesame longitudinal zone.

In still a further alternative, each individual flute-forming bar212,222 or groups of them may be provided with independent fluid-flowcontrol, e.g. using pressure regulators or mass-flow controllersprovided in-line with the distribution manifold (e.g. channel passage203) for each flute-forming bar 212,222 but downstream of the supplymanifold 280 (not shown). In this embodiment pressures and flow rates ofweb-supporting fluid can be individually controlled for eachflute-forming bar 212,222. This could be desirable, for example, if aweb-tension spike is detected downstream of the forming device 200 atonly a discrete lateral (cross-machine) position in the web. In thatevent, the fluid pressure/flow rate of only the forming bars 212,222 atthe associated cross-machine position might be increased based on afeedback control system to provide additional cushion and thus reducefriction at that location.

In each of the foregoing embodiments, a pressurized fluid such as air orsteam is delivered to the supply manifolds 280 via the ports 285 usingappropriate hoses, piping or tubing, which are conventional. Thepressurized fluid travels through the supply passage 282, throughrespective supply openings 283 and into distribution manifoldsassociated with each of the flute-forming bars 212,222, ultimately beingemitted via the associated fluid ports 205. The fluid thus provides afluid cushion (e.g. air) above each flute-forming bar 212,222 on whichthe traveling web 10 can be supported or float as it traverses theintermediate longitudinal fluting labyrinth 250 in the forming device200. The cushion provides air-greasing (i.e., lubrication) that canreduce or eliminate sliding frictional contact between the web 10 andthe forming bars.

In addition to minimizing friction encountered by the web 10 as ittraverses the labyrinth 250, operating the forming bars 212,222 in thezero-contact mode described here can provide an elegant mechanism offeedback control for the mean web tension via an active or passivepressure transducer (not shown) that can be used to detect the pressurein the air cushion under the web 10. Air-cushion pressure and webtension are related according to the relation P=T/R. Thus, monitoringthe air cushion pressure, P, provides a real-time measure of the tensionin the web. Additionally, in the zero-contact mode the cushion of airbetween each of the forming bars 212,222 and the traveling web 10provides a mechanism of instantaneous damping of minute tensionfluctuations in the web, because the web is free to dance above theforming bars on the cushion of air in response to transient and minutetension variances. The result is that the web is less affected by suchtransient tension variances. Finally, it is important to mention that“zero-contact” is not meant to imply there can never be any contact(i.e. literally “zero” contact) between the flute-forming bars 212,222and the web 10. Even operated in the zero-contact mode as describedhere, some contact may occur due to transient or momentary fluctuationsin mean web tension, or in localized web tension, of sufficientmagnitude.

In addition or alternatively to operating in the zero-contact mode asdiscussed above, the web-engagement portions 262 of the forming bars212,222 can include other features designed to minimize or eliminatefriction. In one example, the surfaces of engagement portions 262 can bepolished or electro polished in order reduce the frictional forces onthe web as it is passing through the fluting labyrinth 250. In anotherexample, those surfaces can be coated with a release or antifrictioncoating such as PTFE (Teflon®) or similarly low-friction material inorder reduce the coefficient of friction at the surfaces and thus toreduce frictional forces between them and the passing web 10. In anotherexample, those surfaces can be treated to create a hard surface coatingsuch as by black oxide conversion coating, anodizing, flame spraying,deposition coatings, ceramic coating, chrome plating, or other similarsurface treatments in order reduce the coefficient of friction.

In operation as best seen in FIGS. 7 and 7 a, the forming device 200receives a substantially planar web 10 (e.g. a preconditioned web 10 a)at its rear or entry end 201. On entry into the forming device 200, theweb 10 is full width because it is still planar, and none of its widthhas yet been taken up by longitudinal fluting. In use the degree ofinterlacement of the opposing flute-forming bars 212 and 222 is adjustedat the forward or exit end 202 to fix the lateral take-up ratio of theformed web 10 b on exiting the forming device. For example, followingare typical or traditional take-up ratios for a number of conventionalflute sizes:

Standard Flute Size Take-up Ratio A 1.56 C 1.48 B 1.36 E 1.28 F 1.19 N1.15

Thus, in case it is desired to ultimately produce alongitudinally-corrugated web having, e.g., conventional A-size flutes,the starting width of the initial flat web 10 should be 1.56 times thefinal desired width of the longitudinally-corrugated web to be made inthe corrugating line 1000. Accordingly, if a 50-inch wide longitudinallyA-fluted web is desired, then the starting flat web width should be 78inches wide (1.56×50 inches). Similar calculations could be performedfor other standard flute sizes based on the desired finished web widths.In each case, the forming device 200 can be used to reduce the width ofthe flat web 10 from its initial width (e.g. 78 inches for an A-flutedlongitudinally-corrugated web) to the final, narrower width of thedesired web (e.g. 50 inches for the A-fluted web).

The web 10/10 a is fed into the forming device 200 from the rear/entryend 201 in the machine direction, so that the web passes between theopposed sets 210 and 220 of flute-forming bars 212 and 222. The positionof the first frame 215 is adjusted relative to the second frame 225 atthe forward/exit end 202 so that the degree of interlacement of theopposing bars 212 and 222 produces a serpentine lateral path (i.e. inthe cross-machine direction, best seen in FIG. 3a ) sufficient toconsume the desired proportion of web width so that the formed web 10 bexiting the forming device will have a width that is or approximatesthat of the desired finished web 10 d. In other words, the degree ofinterlacement of the forming bars 212 and 222 at the exit end 202dictates the degree to which the width of the initial web 10 is gatheredto produce a formed web 10 b on exiting the device 200 as seen in FIG.7a . The greater the degree of interlacement at the exit end 202, themore web material will be consumed in the cross-machine direction as theweb negotiates the interlaced forming bars 212 and 222 while travelingin the machine direction.

It is also preferred that the position of the first frame 215 isadjusted at its rear or entry end 201 relative to the second frame 225.Specifically, once the degree of interlacement at the exit end 202 hasbeen fixed, the position of the first frame 215 is adjusted at the entryend 201 (relative to the second frame 225) to select the location of achoke point 290 along the machine direction where the opposed bars 212and 222 just begin to interlace. In operation the choke point 290 iswhere the entering web 10/10 a first contacts or encounters the opposedfirst and second flute-forming bars 212 and 222 uniformly across itsentire width as seen in FIG. 7, as well as in FIG. 5. In FIG. 7, the web10 is illustrated gaining height as the longitudinal flutes are formedin the labyrinth 250. The web height begins to increase ahead of thechoke point 290 in the illustrated embodiment because as the web ispositively fluted at that point, a portion of the web upstream of thechoke point 290 may be induced to assume or to begin conforming to afluted configuration, as well.

The location of the choke point 290 is selected based on the width ofthe entering web 10/10 a, so that at or adjacent the choke point 290 thelateral edges of the entering web encounter and are positioned adjacent(or contact or are supported by) ones of the forming bars 212 and 222whose lateral spacing at the exit end 202 (based on their curvature fromthe choke point forward) defines or approximates the desired width ofthe formed web 10 b on exiting the forming device 200. In this manner,the lateral edges of the entering web 10/10 a will follow the curvatureof the respectively adjacent forming bars 212 and 222 in the machinedirection as they converge laterally on approaching the exit end 202 ofthe forming device, and will be spaced apart by the desired width of theformed web 10 b on exiting that device 200.

This will be further understood with reference to FIG. 5, whichillustrates a schematic top view of the interlaced array of opposedforming bars 212 and 222, wherein the bars are represented by contourlines. As seen in the figure, initial webs 10/10 a are depictedschematically entering the interlaced array from the entry end 201 inorder to be longitudinally fluted to an intermediate geometry to producea formed web 10 b having a desired final width. The initial web marked“A” indicates a web intended to produce a longitudinally A-fluted web atthe illustrated final width, and the initial web marked “C” indicates aweb intended to produce a longitudinally C-fluted web at the finalwidth. (Note that FIG. 5 and the take-up ratios therein are not toscale; the figure is for illustrative purposes only). From the tableabove, a typical take-up ratio for A-flutes is 1.56, and for C-flutes is1.48. Although not to scale, the figure shows that to achieve a formedweb 10 b of the same final width, an initially wider web will berequired if A-flutes are to be introduced downstream than for C-flutes,because A-flutes demand a greater take-up ratio.

As discussed above, the final interlacement of the opposingflute-forming bars 212 and 222 at the exit end 202 will define thetake-up ratio in the forming device 200. Separately, the choke point 290is selected based on the initial width of the entering web 290 asdiscussed above. In FIG. 5 the width of the “A” initial web 10/10 acorresponds to the spacing of the two outermost forming bars 212,222 allthe way at the rear/entry end 201 of the forming device 200. Thus thechoke point 290 can be positioned at or adjacent the entry end 201because as the lateral edges of the “A” web proceed in the machinedirection, they will follow contour lines along the curvature of theadjacent forming bars 212 and 222 and thus converge to the final desiredwidth of the formed web 10 b at the exit end 202. However, because the“C” initial web 10/10 a is narrower the choke point 290 is adjusteddownstream in the machine direction so that the “C” web's lateral edgeswill first encounter ones of the forming bars 212,222 that at the exitend 202 will define or approximate the final desired width of the formedweb 10 b. In the situations illustrated in FIG. 5, the opposed sets offorming bars 210 and 220 would be adjusted so that the choke point 290for the respective “A” or “C” web is coincident with or adjacent wherethe outer edges of the respective web also encountering the laterallyoutermost flute-forming bars 212,222. This would be desirable, forexample, when the distance between the outermost forming bars 212,222 atthe exit end 202 corresponds to the desired width of the formed web 10b. Thus as will now be appreciated, the distance between the outermostforming bars 212,222 at the exit end 202 can be selected to correspondto a desired standard width for longitudinally-corrugated websregardless of the corrugation pitch. When configured this way, the chokepoint 290 for a given initial web width would routinely be adjusted tocoincide with or to be adjacent the location where the web's outer edgeswould encounter the laterally outermost flute-forming bars 212,222.

It is noted that for a given web and take-up ratio combination, someroutine iteration may be desirable to optimize the location of the chokepoint 290 once the take-up ratio has been fixed at the exit end 202, toaccount for variable degrees by which different webs might be induced tocommence a fluted configuration upstream of the choke point. In suchinstances, the choke point location should be selected to ensure thatlittle or no cross-machine translation of the web occurs over orrelative to the flute-form ing bars 212,222, at least at locations incontact with flute-forming bars. In most instances, the curvature of thebars 212,222 should prevent this even in cases when the web is inducedto begin assuming a fluted configuration upstream of the choke point.But some iteration may be desirable in such cases.

It will be appreciated that in operation, as a web traverses the flutinglabyrinth 250 in the machine direction, its width is gathered in thecross-machine direction through the gradual formation of a full-widtharray of longitudinal flutes of intermediate geometry. As the webprogresses through the labyrinth 250 the array of intermediate-geometryflutes are gradually and uniformly introduced (i.e. substantiallycontemporaneously across the full width of the web) into the web as thedegree of interlacement of opposing flute-forming bars 212,222 increasesfrom the choke point 290 forward, and as those bars converge in thecross-machine direction based on their curvature. Based on the curvatureof the flute-forming bars 212 and 222, substantially no portion of theweb must traverse any of those bars in a cross-machine direction inorder to converge in that direction to gather (i.e. reduce) web width.Rather, individual elements of the web follow the convergent, curvedcontour lines of the forming bars 212 and 222, or curved contour linesbetween adjacent ones of those forming bars, so that they experienceonly machine-direction translation relative to the forming bars 212 and222 and no cross-machine-direction translation relative to those bars orany other flute-form ing element. As a result, zero or substantially nolateral friction or tension forces, or lateral friction or tensionfluctuations are introduced into the web as it traverses the flutinglabyrinth 250 because the web is not stretched or pulled laterally as itpasses through that labyrinth 250. In other words, in the forming device200 no portion of the web 10 must negotiate an undulating pathwaybounded by forming bars 212 and 222 in a lateral direction as ittraverses one or more flute-forming bars or other flute-forming elementsin that direction. When operated in a zero-contact mode as describedabove, machine-direction tension fluctuations can also be reduced oreven eliminated because if the web does not contact the forming bars 212and 222 there will be no friction between them. Thus, substantiallyevery element of the traveling web moves in three dimensions (e.g.,laterally, vertically and forward) simultaneously, while alsomaintaining substantially constant cross machine tension andmachine-direction tension because the forming device 200 does notintroduce lateral or longitudinal tension fluctuations in the travelingweb even though it introduces longitudinal flutes therein to gather webwidth. Upon exiting the forming device 200 the width of the formed web10 b is adjusted to conform to or approximate the final width of adesired longitudinally-corrugated or other three-dimensional web to bemade in a downstream operation, based on the lateral take-up ratiorequired to accommodate the final three-dimensional configuration.

FIG. 8 illustrates an alternative embodiment of a forming device 200,wherein the forming device not only gathers web width 10 but alsoconducts that web through a curved web pathway to adjust the course ofthe formed web 10 b on exiting the forming device 200 relative to theentering web 10/10 a. In this embodiment, the flute-forming bars 212 ofthe first set 210 have radiused portions that curve about an imaginaryaxis parallel to the cross-machine direction such that the radiusedportions together define a substantially partially cylindrical archaving a first radius of curvature R₁ between said axis and bars 212. Itis noted that the aforementioned curvature having radius R₁ relative tothe noted imaginary axis is independent of and in addition to theconvergent curvature of individual forming bars 212 in the first set 210discussed above. That is, in this embodiment the forming bars 212 willboth bend around the partially cylindrical arc noted above and graduallyconverge as described above to provide simultaneous course correctionand web-width gathering for the traveling web. Likewise, the flute-forming bars 222 of the second set 220 have cooperating radiused portionsthat curve about another imaginary axis parallel to the cross-machinedirection such that the radiused portions of the flute forming bars 222similarly define a substantially partially cylindrical arc having asecond radius of curvature R₂. And likewise, this curvature based on theradius R₂ is independent of and in addition to the convergent curvatureof individual forming bars 222 in the second set 220 as discussed above.

The arc lengths for each of the first and second sets 210 and 220 of theforming bars 212 and 222 are selected so that the desired courseadjustment of the web-travel pathway can be achieved while traversingthe longitudinal fluting labyrinth 250. For example, for a 90° coursecorrection the arc length of the sets 210 and 220 of forming bars aresuch that the fluting labyrinth 250 defined between them follows acourse that extends π/2 radians at the desired radius of curvature. Thisembodiment may be desirable, for example, where it is desired to savespace by feeding the initial web 10/10 b from above the forming device200 rather along a linear web path. As will be appreciated, othergeometries and curvatures (e.g. twisting) of the forming-bar arrays 210and 220 are possible and can be selected based on the geometry of aparticular installation and the resultant desired web-travel pathway.

Corrugating Die

On exiting the forming device 200 the formed web 10 b can be fed to acorrugating die 300 as illustrated in FIG. 9a . The corrugating die 300includes first and second die halves 310 and 320 and has an entry end301 and an exit end 302 as shown. The first die half 310 has a formingsurface 315 for converting the formed web 10 b that emerges from theforming device to a near net-shaped web 10 c having a flutedconfiguration that approximates the final desired corrugations of afinished web 10 d. At or near the entry end 301 of the corrugating die300 the first forming surface 315 has a series of large-amplitudelongitudinal ribs 316 defining a lateral cross-section that has asubstantially sinus-wave configuration whose frequency and amplitudesubstantially correspond to or approximate those of the intermediateflutes imparted to the formed web 10 b in the forming device 200. As theforming surface 315 proceeds in the machine direction, the sinus contourof the large-amplitude ribs 316 gradually evolves into a final sinuscontour (in lateral cross-section) at the exit end 302, defined bysmall-amplitude longitudinal ribs 318 and the alternately intermediatevalleys between them. It will be appreciated that the forming surface315 is a continuous and smooth surface, which smoothly and graduallytransitions from the large-amplitude sinus contour at the entry end 301to the small (near-net shape) amplitude sinus contour at the exit end302. As seen in FIG. 9a the small-amplitude ribs 318 gradually andsmoothly emerge without abrupt transitions from the large-amplitude ribs316 and are formed in the machine direction until ultimately theyentirely replace the original surface contour at the entry end 301formed by the large-amplitude ribs 316. The ribs 318 are dimensioned sothat the frequency and amplitude of the sinus contour of the formingsurface 315 at the exit end 302 represents a near-net shape thatapproximates the final desired corrugations for the finished web 10 d.The second die half 320 also has a forming surface configured asdescribed above, which opposes and is the substantial complement of theforming surface 315 in the first die half 310.

Referring now to FIGS. 9b and 9c , the forming surface 315 of at leastone of the die halves (e.g. first die half 310 in FIG. 9b ) has atapered portion 312 at the entry end 301, which tapers gradually towardthe forming surface of the opposite die half (half 320 in FIG. 9b )along the machine direction until the opposing forming surfaces areuniformly spaced apart along the machine direction. As seen in thefigure, the tapered portion is composed of the large-amplitude ribs 316discussed above, which taper toward the opposite die half (preferably ata constant slope) when viewed from the side until they reach and areinterlaced with the opposing large-amplitude ribs 316 at the oppositeforming surface. In this manner, the tapered portion 312 cooperates withthe forming surface of the opposite die half to form a mouth 330 at theentry end of the corrugating die 300, into which the formed web 10 b canbe fed. The mouth 330 avoids an abrupt transition for the web 10 b whenentering into the corrugating space between the opposing die halves 310and 320, and instead provides for a gradual transition. In analternative embodiment, the respective forming surfaces of the opposingdie halves can each have oppositely-tapered portions to form the mouth330 instead of only one of the die halves having a tapered portion 312.

In operation, the die halves 310 and 320 are engaged as shown in FIG. 9band the formed web 10 b enters the corrugating space between theopposing forming surfaces thereof via the mouth 330. As the web passesthrough the corrugating die 300, the formed web 10 b from the formingdevice 200 is converted into a near net-shaped web 10 c thatapproximates the final corrugated web 10 d as the large-amplitude ribs316 gradually give way to the small-amplitude ribs 318 therein. Inparticular, as the web progresses its shape gradually evolves from aninitial sinus contour defined by the relatively large-amplitude,low-frequency intermediate-geometry flutes (corresponding to the contourof the large-amplitude ribs 316), into a final sinus contour at the exitend 302 having a relatively higher frequency and lower amplitudecorresponding to the small-amplitude ribs 318. The final sinus contourof the web 10 c on exiting the corrugating die 300 constitutes a nearnet shape for the web that approximates the final desired corrugatedgeometry. Preferably, the web contour smoothly and gradually transitionsfrom the large-amplitude initial sinus contour to the small (near-netshape) amplitude sinus contour as it passes between the opposed firstand second complementary forming surfaces, following the gradual andsmooth transition from the interlocking large-amplitude ribs 316 thereinto the interlocking small-amplitude ribs 318. This progression of theweb can be seen in FIG. 10, which illustrates a portion of the web as ittraverses the corrugating space between the forming surfaces 315, and issmoothly transitioned from the fluted configuration at 10 b to thenear-net shape at 10 c. Importantly, the width of the near net-shapedweb 10 c is approximately the same as the formed web 10 b as it entersthe corrugating die 300; i.e. w_(i)≈w_(o) in FIG. 10. As a result,lateral tension forces and stresses that might otherwise be imparted tothe web 10 in the corrugating die 300 (as a result of forming the nearnet-shaped sinus pattern therein) are substantially reduced oreliminated. Because the initial and final widths of the web through thecorrugating die 300 are substantially the same, no portion of the webneeds to move laterally (in the cross-machine direction) in order toform the higher-frequency, lower-amplitude flutes (at 10 c) from thelower-frequency, higher-amplitude flutes (at 10 b). Instead, individualelements of the web need only translate vertically as the web travels inthe machine direction, and not laterally. As a result, because there issubstantially no lateral movement of individual web elements thecorrugating die introduces substantially no lateral tension orfrictional forces or fluctuations to the web. This reduces the chancesof damaging the web.

In FIG. 9a die halves 310 and 320 are illustrated separated from oneanother to allow visualization of the contour of the die's internalforming surfaces. But in use the die halves 310 and 320 are brought intoengagement with one another as seen in FIGS. 9b and 9c and discussedabove, wherein the second die half 320 has an internal forming surfacethat is the complement of the forming surface of the die half 310, alsomentioned above. Preferably, when so engaged there is a constant orsubstantially constant spacing between the opposing die halves 310 and320, and their respective and complementary forming surfaces, so thatthe traveling web 10 is not compressed to any significant degree as ittraverses the corrugating die 300. In particular, the spacing betweenthe opposing and complementary forming surfaces downstream of thetapered portion(s) 330 thereof preferably is constant and uniform, andpreferably is at least 150% the thickness of the web that will traveltherebetween, more preferably at least 175% that thickness, and mostpreferably at least 200% or 250% that thickness; in any event thespacing preferably is not greater than 400% that thickness. Thus thedegree of drag on the traveling web can be greatly reduced compared toif the spacing between the opposed forming surfaces were selected tojust correspond to the approximate thickness of the web.

Moreover, to operate the corrugating line 1000 continuously it will benecessary periodically to splice the web 10 in order to sustain aconstant supply of medium material in a continuous and uninterrupted web10. The maintenance of the aforementioned spacing between the opposingdie halves will permit periodic splices in the web 10 to pass throughthe forming die 300 without incident, and to be formed into the nearnet-shaped web 10 c with the rest of the continuous web. In practice,the respective die halves 310 and 320 can be mounted to frames (notshown), which will support them and maintain a relative distance betweenthem when engaged to afford the modest degree of spacing between theopposed forming surfaces as discussed above.

To further reduce drag and the introduction of longitudinal tensionfluctuations, the corrugating die halves 310 and 320 can be providedwith an array of fluid ports 305 over their respective forming surfaces,through which a pressurized fluid similarly as described above can bedelivered to provide a fluid cushion for supporting the web on eitherside. Also similarly as above, supply manifolds 380 can be distributedon each of the first and second die halves 310 and 320, connected to afluid supply and provided in fluid communication with the fluid ports inthe associated die half 310 or 320, or with respective banks of thoseports in respective longitudinal zones along the machine direction. Themanifolds 380 can be arranged, configured and operated analogously asdescribed above in order to selectively supply fluid flow rates andpressures uniformly to the fluid ports in each of the first and seconddie halves 310 and 320, or to different longitudinal zones uniformly inthe same longitudinal zone(s) in both die halves 310 and 320. In thismanner, the fluid cushion can minimize or prevent frictional lossesbetween the traveling web and the forming surfaces of the die halves 310and 320 by reducing or even inhibiting contact between them as the webtravels.

It is contemplated that corrugating dies having forming surfaces ofdifferent contours can be selected and used based on a) the particularsinus pattern of the formed web 10 b to be introduced therein, and b)the final desired flute size for the finished web. Thus differentcorrugating dies 300 can be provided corresponding to differentcombinations of take-up ratio (corresponding to desired final flutesize) and final web width, and can be interchanged in the corrugatingline 1000 when different webs are to be made. It is contemplated, forexample, that several corrugating dies 300 can be made based onstandardized web sizes and flute pitches to be interchangeably installeddownstream from a forming device 200 and upstream of a final corrugatingapparatus 400.

Finally, it is noted that the corrugating die 300 described here ispreferred in select embodiments, but it is considered optional in thecorrugating line 1000. That is, while the corrugating die 300 may bedesired to gradually convert the intermediate-fluted, formed web 10 b tothe near net-shaped web 10 c that approximates a final corrugated web 10d, in embodiments it may be possible or desirable to simply feed theformed web 10 b directly into a final corrugating apparatus, e.g.longitudinal corrugating rollers, to impart the final longitudinalcorrugations or other three-dimensional structure therein.

Final Corrugating Apparatus

On exiting the corrugating die 300 (if present) or the forming device200, the formed or near net-shaped web 10 b or 10 c can be delivered toa final corrugating apparatus 400 to yield the final corrugated web 10 dhaving the desired longitudinal corrugations at the desired final webwidth. In one embodiment the final corrugating apparatus includes a pairof longitudinal corrugating rollers 410 and 420 as seen in FIG. 11. Inthis embodiment, the corrugating rollers 410 and 420 are each journaledon respective rotational axes 411 and 421 that are parallel to oneanother and perpendicular to the machine direction when viewed fromabove, such that the web-travel pathway passes between the opposedrollers 410 and 420. The rollers 410 and 420 have respective andcomplementary sets of circumferentially extending and longitudinallydistributed ribs, such that at a nip 450 between the rollers 410 and 420the ribs of one roller extend and are received within the valleysdefined between the opposing ribs on the opposite roller, and viceversa. The opposing ribs are selected so as to define between them asubstantially sinus nip 450 having a contour in the lateral directionthat corresponds in frequency and amplitude to the desired flutes forthe longitudinally-corrugated web 4 d.

In operation the formed web 10 b or near net-shaped web 10 c is fedalong the machine direction into and through the nip 450 between thecorrugating rollers 410 and 420. The web 10 b/10 c pass through the nip450 and is compressed between the opposing rollers 410 and 420 to formand relax the web in the sinus, longitudinally-corrugated shape so thatthe final corrugated web 10 d will retain that shape independently fromthe application of any external corrugating force or when that force isremoved. Whether the web entering the corrugating nip 450 is a formedweb 10 b directly from the forming device 200 or a near net-shaped web10 c from a corrugating die 300, its width remains substantially thesame prior to, while and after traversing the corrugating nip 450. As aresult, again there are preferably no or substantially no net lateralforces (cross-machine direction) on the web as it is corrugated at thecorrugating nip 450.

The finished corrugated web 10 d can then be fed to additional units oroperations for further downstream processing. For example, thecorrugated web 10 d can be delivered to a conventional single-faced asknown in the art, in order to apply a liner to produce a conventionalsingle-faced web. That single-faced web can then be fed to adouble-backer to apply a second liner to the remaining exposed flutecrests of the web to produce conventional double-wall corrugated board,which can then be cut and shaped in a conventional manner to makepackaging material, such as boxes.

CONCLUSION

Conventionally, the friction experienced by a paper web proceedingthrough a longitudinal corrugating machine (as disclosed in U.S. Pat.Appl′n Pub. No. 2010/0331160) was large enough to damage the paper web.This occurred because the amount of friction experienced by thetravelling web, as it was gathered inward (i.e. its width reduced toaccommodate the longitudinal corrugations), increased exponentially withthe number of flute-forming bars against which the paper web wasrequired to travel in the transverse, non-machine direction. Thusexisting longitudinal forming devices would apply an ever-increasingamount of friction and oscillatory and transitory lateral-tension forcesto the paper web that can ultimately deform and/or destroy the endproduct.

Conversely, the curved (e.g. parabolic) geometry of the flute-formingbars 212 and 222 of the forming device 200 described here yield agradual forming process that uniformly and continuously forms theinitial web into an intermediate sinusoidal shape having a reduced widthcorresponding to the desired take-up ratio, but without introducingtransient or fluctuating lateral-tension forces. Because individual webelements follow a continuous curved path along curved contour linesdefined by the curved flute-forming bars (see FIG. 5), there issubstantially no lateral movement in the web relative to theflute-forming bars 212,222. In other words, the curved forming bars212,222 are designed such that each portion of the web (e.g. paper web)will follow substantially the same forming bar, or a continuously-curvedcontour line between adjacent forming bars 212,222, along the machinedirection from the entry end 201 to the exit end 202 of the formingdevice 200. As a result, the traveling web preferably experienceslittle, if any, movement in the transverse, cross-machine directionrelative to the forming bars 212,222. This means that little, if any,net friction or tension forces or associated fluctuations is/are appliedto the traveling web in the forming device 200 along the transverse,non-machine direction.

Although particular embodiments of the invention have been described indetail, it will be understood that the invention is not limitedcorrespondingly in scope, but includes all changes and modificationscoming within the spirit and terms of the claims appended hereto.

What is claimed is:
 1. A forming device having an entry end and an exitend spaced apart along a machine direction, the forming devicecomprising first and second sets of flute-forming bars opposing oneanother and defining therebetween a longitudinal fluting labyrinth, eachsaid set of flute-forming bars extending from adjacent said entry endtoward said exit end, at least respective subsets of said flute-formingbars in each of said first and second sets thereof being curved suchthat the bars in each said respective subset converge in a cross-machinedirection as a result of their curvature as they proceed toward saidexit end.
 2. The forming device of claim 1, each of said subset offlute-forming bars being curved in at least a rear portion thereofbeginning adjacent said entry end, and having a degree of curvature thatdecreases along the length of said rear portion in a direction towardsaid exit end.
 3. The forming device of claim 2, wherein tangents of allof said flute-forming bars at a location adjacent said exit end are allsubstantially parallel along said machine direction.
 4. The formingdevice of claim 1, each of said subset of flute-forming bars beingcurved such that they all converge laterally toward a common imaginaryline that runs parallel to said machine direction.
 5. The forming deviceof claim 4, said imaginary line being a centerline of said formingdevice extending along said machine direction.
 6. The forming device ofclaim 1, wherein a spacing between said first and second sets offlute-forming bars is adjustable adjacent said exit end to at leastpartially interlace the opposing sets of flute-forming bars adjacent theexit end.
 7. The forming device of claim 6, said spacing also beingadjustable adjacent said entry end to thereby adjust a machine-directionlocation of a choke point where the opposing first and second sets offlute-forming bars begin to interlace.
 8. The forming device of claim 1,said first set being a first planar array of flute-forming bars, saidsecond set being a second planar array of flute-forming bars, whereincurved flute-forming bars in said first planar array all converge withrespect to a first imaginary centerline in said first planar array, andwherein curved flute-forming bars in said second planar array allconverge with respect to a second imaginary centerline in said secondplanar array.
 9. The forming device of claim 8, wherein at any givenlocation along said machine direction, all of the flute-forming bars insaid first planar array are equidistant from one another and all of theflute-forming bars in said second planar array are equidistant from oneanother.
 10. The forming device of claim 9, said first and second planararrays being arranged such that when viewed from above all of theflute-forming bars from both said arrays together are equidistant fromone another in the cross-machine direction at any givenmachine-direction location.
 11. The forming device of claim 8,comprising a linear flute-forming bar in at least one of said first andsecond planar arrays, aligned and collinear with the respective first orsecond imaginary centerline therein.
 12. The forming device of claim 1,wherein curved flute-forming bars in a respective one of said sets havea degree of lateral curvature that decreases in the machine directionsuch that rates of lateral convergence thereof also decrease until amachine-direction location where imaginary tangents of each of theflute-forming bars in the respective set all become substantiallyparallel along the machine direction, said tangents remainingsubstantially parallel through said exit end.
 13. The forming device ofclaim 12, wherein at any given location along said machine direction,all of the flute-forming bars in each of said respective sets areequidistant from one another.
 14. The forming device of claim 13, saidfirst and second sets of flute-forming bars being interlaced beginningat a choke point spaced from said entry end along the machine direction,with a degree of interlacement of said arrays gradually increasing fromsaid choke point toward said exit end.
 15. The forming device of claim1, said first set being a first planar array of flute-forming bars andsaid second set being a second planar array of flute-forming bars. 16.The forming device of claim 1, said first set defining a first array ofsaid flute-forming bars and said second set defining a second array ofsaid flute-forming bars, said first and second arrays each being curvedto define respective substantially partially cylindrical arcs havingrespective radii of curvature relative to imaginary first and secondcross-machine axes, such that at least portions of the flute-formingbars in each of the respective arrays are radiused relative to therespective imaginary cross-machine axis in addition to being laterallycurved in order to converge laterally along the machine direction. 17.The forming device of claim 1, a plurality of said flute-forming barseach having a plurality of fluid ports therein configured to emit afluid to provide a fluid cushion between said bars and a web travelingthrough said forming device in operation.
 18. A method of forming alongitudinally-corrugated web, comprising: uniformly introducing into aweb of medium material a full-width array of longitudinal flutes of afirst geometry as the web travels along a web-travel pathway in amachine direction, thereby reducing the width of said web tosubstantially a final width that corresponds to a take-up ratio forpreselected longitudinal corrugations or other three-dimensionalstructure to be formed in the web, wherein at any selected locationalong said web-travel pathway said longitudinal flutes define a sinewave that propagates in a cross-machine direction and has a constantzero-crossing point.
 19. The method of claim 18, further comprising,after introduction of said first-geometry flutes into said web,introducing therein longitudinal corrugations having a lower amplitudeand higher frequency than said first-geometry flutes, and relaxing theweb so that it will independently retain said longitudinal corrugations.20. The method of claim 19, wherein between introduction of saidfirst-geometry flutes and said longitudinal corrugations, a lateralcontour of said web smoothly evolves from an initial sinus contourdefined by said first geometry flutes to a final sinus contour thatapproximates a geometry of said longitudinal corrugations.
 21. Themethod of claim 20, wherein individual elements of the web need onlytranslate in a direction normal to a plane extending generally along theweb-travel pathway and not laterally in a cross-machine direction as theweb's lateral contour evolves from said initial sinus contour to saidfinal sinus contour.
 22. A method of forming a longitudinally-corrugatedweb, comprising: a) feeding a web of medium material having an initialwidth in a machine direction through a longitudinal fluting labyrinthdefined between opposing sets of at least partially interlacedflute-forming bars, wherein pluralities of the flute-forming bars ineach set are curved such that the bars in said respective pluralitiesconverge in a cross-machine direction as a result of their curvature asthey proceed toward an exit end; and b) reducing the width of said webto a substantially final width by forming longitudinal flutes of a firstgeometry in said web as it passes through said labyrinth.
 23. The methodof claim 22, said opposing sets of flute-forming bars having a degree ofinterlacement that increases in the machine direction beginning at achoke point where said sets just begin to interlace and continuing untilsaid exit end, wherein said intermediate-geometry longitudinal flutesare thereby gradually formed between said choke point and said exit end.24. The method of claim 23, further comprising adjusting the degree ofinterlacement at said exit end so that said initial width is greaterthan said final width by a take-up ratio corresponding to preselectedfinal corrugations or other three-dimensional structure to be introduceddownstream in said web while retaining said final width.
 25. The methodof claim 24, further comprising adjusting a spacing between saidopposing sets of flute-forming bars at an entry end where said webapproaches said labyrinth to thereby adjust a machine-direction locationof said choke point.
 26. The method of claim 22, said first and secondsets of flute-forming bars comprising respective first and second arraysof said bars, each said array having an imaginary centerline along themachine direction, wherein all of the bars in each said array that arelaterally spaced from said centerline converge in the cross-machinedirection toward said centerline as a result of their curvature.
 27. Themethod of claim 26, wherein all the bars in each said array convergeuntil a machine-direction location where imaginary tangents of all ofthe flute-forming bars in the respective array become substantiallyparallel along the machine direction, said tangents remainingsubstantially parallel through said exit end.
 28. A forming devicehaving an entry end and an exit end spaced apart along a machinedirection, the forming device comprising first and second sets offlute-forming bars opposing one another and defining therebetween alongitudinal fluting labyrinth, each said set of flute-forming barsextending from adjacent said entry end toward said exit end, at least asubset of said flute-forming bars having a variable-tangentconfiguration such that imaginary tangents to each of said subset ofbars, at spaced locations along a length thereof, become successivelynearer to parallel with the machine direction such that said subset ofbars converge in a cross-machine direction as a result of saidvariable-tangent configuration as they proceed toward said exit end. 29.The forming device of claim 28, wherein tangents of all of saidflute-forming bars at a location adjacent said exit end are allsubstantially parallel along said machine direction.
 30. The formingdevice of claim 28, each of said subset of flute-forming bars convergingtoward a common imaginary line that runs parallel to said machinedirection.
 31. The forming device of claim 28, wherein a spacing betweensaid first and second sets of flute-forming bars is adjustable adjacentsaid exit end to at least partially interlace the opposing sets offlute-forming bars adjacent the exit end.
 32. The forming device ofclaim 31, said spacing also being adjustable adjacent said entry end tothereby adjust a machine-direction location of a choke point where theopposing first and second sets of flute-forming bars begin to interlace.33. The forming device of claim 28, said first set being a first planararray of flute-forming bars, said second set being a second planar arrayof flute-forming bars, wherein variable-tangent flute-forming bars insaid first planar array all converge with respect to a first imaginarycenterline in said first planar array, and wherein variable-tangentflute-forming bars in said second planar array all converge with respectto a second imaginary centerline in said second planar array.
 34. Theforming device of claim 33, said first and second planar arrays beingarranged such that when viewed from above all of the flute-forming barsfrom both said arrays together are equidistant from one another in thecross-machine direction at any given machine-direction location.
 35. Theforming device of claim 33, said first and second arrays offlute-forming bars being interlaced beginning at a choke point spacedfrom said entry end along the machine direction, with a degree ofinterlacement of said arrays gradually increasing from said choke pointtoward said exit end.